Macroeconomics, Representative Agents and Demographics (wonkish)
Upon first reading what I am pasting below, my thesis councillor briskly claimed that this particular piece of text represented a malignant tumor that had to be surgically removed if the patient (in this case, my master’s thesis) were to make it alive. I agreed with him back then and I still do, but I thought that the section was too interesting to be entirely destined to the dustbin. Moreover, the debate on the state of macro has got new life on the back of the financial and economic crisis with a lot of interesting contributions in the past 1 1/2 and 2 years  and I wanted to add my own spin on, at least, a small part of the issues involved.
The impetus for the the discussion below essentially came as I realized that the only way that I could meaningfully attempt to stand on the shoulders of giants in terms of mapping a relationship between ageing and capital flows was through the use of representative agent models and thus through the use of classic macroeconomic microfoundations. This is natural logic for any trained macroeconomist, but I started out believing that my specific problem demanded a different theoretical approach and it led to a discussion on the merits of the representative agent.
So without further ado …
The Macroeconomics of Demographics: do we need micro foundations?
One key proposition for this thesis is that the demographic transition needs to be rethought or perhaps more aptly reformulated Edward Hugh (2006). Although this is certainly not a new proposition, it is important to emphasize in the context of the applying a model (idea) of the DT as a foundation for economic analysis. One particularly important feature here is that, while many of the outcomes of the demographic transition may be operationalized in the context of economic phenomena (and thus theory), economic theories cannot, alone, explain the underlying processes which give rise to these economic facts.
This presents us with a rather unique challenge. On the one hand economic convention demands that results and modeling be expressed in a sometimes rigid and arcane mathematical language, but this may not always be appropriate. Consequently, considerable complexity on the conceptual level may be lost in the transition from complex empirical regularities to formal economics. As a result, the idea that a proper understanding of demographic transitions demands an interdisciplinary approach in relation to economics is a key proposition for this thesis, but also one which is difficult to adhere to as the theoretical framework through which most ideas on macroeconomics and demographics are expressed remains the classical framework with utility maximizing representative agents whose behavior in optimum is aggregated to the macro-economy.
In this vein, the main theoretical model used to motivate the empirical analyses in my thesis is the intertemporal current account  and in this context, the notion of intertemporal optimality and intertemporal optimization are key principles. The idea of the intertemporal choice has long lasting roots and the original contribution comes from Fischer (1930) who laid the foundation for the idea that value has both a time and quantity perspective. This fundamental proposition which today forms the backbone of financial and economic theory was later treated by Roy Harrod (Harrod (1939, 1960 and 1963)) to formulate the dynamic theory which later has given rise to the notion that the utility of consumption in two periods be related via the market (as well as potentially subjective) discount rate. The main idea to recognize here is the fact that income (Y) can only be saved (s) or consumed (c) and that the decision to do so depends on the discounted value of foregoing consumption today relative to tomorrow. The imperative question to answer in the present context is thus how ageing can explain this intertemporal substitution between savings and consumption on an aggregate level. This question was specifically addressed by Modigliani’s life cycle hypothesis Modigliani and Brumberg (1954) and Modigliani and Ando (1963) as well as Friedman’s famous permanent income hypothesis Friedman (1957). These results have been the source of an almost dizzying amount of empirical tests and further theoretical elaborations and this thesis shall try to give as accurate an account of the field as possible.
In a context of economic ideology this framework has been widely used to differentiate Keynes’ original idea that consumers spend out of current disposable income which again has led to a never ending discussion about time horizons. Modigliani’s life cycle hypothesis as well as Friedman’s permanent income hypothesis are exactly examples of such elaborations. And further into the realms of Neo-Classical economics Robert Lucas’ rational expectations hypothesis has further been formulated in the context of the problem above to show the irrelevance of policies to affect output and inflation in short run (The Lucas Critique). This thesis shall neatly sidestep the grand old issue of the short run vs. the long run but rather home in on the principle of intertemporal substitution (or consumption smoothing in the lingo of the theory) and forward looking behavior of economic agents. Specifically the topics under consideration will be the presence of an aggregate economic life cycle of consumption and saving driven by this intertemporality, how this intertemporality manifests itself, and how the divergence in time horizons between consumers, governments, and companies may affect this life cycle. In a concrete context the idea of intertemporal preference between consumption and saving shall be cast in the context of an economy’s preference or tendency to run an external surplus or deficit.
A Benchmark Problem
In the present context, the use of the intertemporal consumption result can be motivated by the following expression of the agent’s maximization problem (1) and her choice in optimum (2);
This is then a simplified version of a representative agent model, but in terms of generalization this problem is a good representation. In this setup (a) is equal to assets, (r) is the interest rate which is assumed constant, (c) is consumption and finally (y) is income ( assumed exogenously given). The value of beta (β) is given by 0< β<1. This variable is a measure of our representative agent’s patience. If beta is equal to 1 consumption tomorrow is of equal value to consumption today and if it is zero our agent only cares about consumption today. The budget constraint simply states that our assets in time (t+1) is equal to the accrued return on our assets in time (t=0) + income minus consumption.
The equation is thus one of the simplest forms of the intertemporal decision by our representative consumer. Solving the problem we get (from equation (2)) the classic result that marginal utility in period (0) depends on the discounted marginal utility in period (t+1); where beta is the subjective discount rate (time preference).
In fact, why don’t we just go ahead and solve the thing so that you can see for yourself what is going on. Now, I am going to go through with brute force here and assume that any readers with no knowledge of calculus will know full well to skip this part . Using the problem above, we can setup the following constrained optimization problem.
The important thing to understand in these kinds of problems is the distinction between state and choice variables. Here the agent chooses assets and consumption given income and the interest rate. This leads to three first order conditions.
The key to solve this problem is first of all to recognize that as always in such an optimization problem we would first of all like to solve out the Lagrange multipliers in order to get a closed form solution. Moreover, we would like to follow in the mental footsteps of Irvin Fischer and Euler and express this solution as a dynamic relationship between consumption in period 0 and period t+1. Fortunately this is quite easy in the present case (setting "s" to 1 in the third step);
This Euler equation shows exactly the relationship I explained above in words, namely that the consumer’s marginal utility in period (t+1) is equal to the marginal utility in period (t) discounted by the market discount rate as well as the subjective discount rate (beta)
The Origins of the Representative Agent
So, if you made it this far and before an actual discussion of whether the representation above is an adequate and useful macroeconomic construct it is worthwhile to trace its origins because its story is a remarkable one. It first appeared in the context of Alfred Marshall’s Principles of Economics in the form of the representative firm Hartley (1996) and Marshall originally conjured this entity in the context of constructing a supply curve for the industry and essentially, as Hartley points out, the creation seemed rather innocent at first.
However, this was not the position taken by Marshall’s peers and after a devastating critique by, among others, John Maynard Keynes and Lionel Robbins the idea of the representative agent was put to rest in the first part of the 20th century Hartley (1996). It would take some 40 years before the idea of the representative agent was resurrected and this time its endurance would prove pervasive.
According to Hartley (1996) the first use of representative agents in a post Marshall perspective has its origins in the period in which neo-classical economics was reaching its zenith. Concretely, Lucas and Rapping (1970) is cited as the first contribution using a representative agent detailing the theory of intertemporal labour supply which is a core assumption of most real business cycle models Romer (2006, ch. 4). Generally, representative agent models are often narrated in the form of an ideal type Walrasian model where the parameters in question are assumed to represent fixed entities which do not change with policy regimes. The model described above is an example of such a model. Apart from adhering to the ideal of constructing a Walrasian equilibrium model, the modern use of representative agents are also closely linked with the idea of rational expectations Sargent (1993), Lucas (1976) and the famous Lucas Critique attacking traditional Keynesian policy evaluation models Hartley (1997, ch. 4) and Lucas (1976). Finally and as David Colander points out in a review of Hartley (1997), the use of representative agents is also closely tied to the pedagogy of macroeconomics Colander (1997).
Ironically however, the occasion for the return of the representative agent to macroeconomics was a widespread need and desire among scholars to provide microfoundations for macroeconomics and thus to differentiate the Keynesian idea of a pure macroeconomic theory. In addition, the modern reincarnation of representative agent models is primarily motivated by the desire to build Walrasian general equilibrium models as well as to imbue agents with rational expectations Lucas (1976). This desire can of course be debated on its own merit, but more interestingly would be to find out whether the use of representative agent models is useful in general. Kirman (1992) and, in particular, Hartley (1997) think that they are not. Especially Hartley (1997) is devastating in his critique and argues that the impetus to construct microfoundations through Walrasian ideal type representative agents with rational expectations fail on a number of critical measures. Key issues here are the representative agent’s inability to model the obvious degree of heterogeneity on a macro level as well as the issue of aggregating the results derived in a microeconomic context. Hartley (1997) thus attempts the ultimate coup-de-grâce;
The idea that we can start with nothing other than individuals maximizing their own utility and build up a model that explains the macroeconomy is nothing but a myth
It is important to note that the discourse fielded in Hartley (1997) and Kirman (1992) is a fringe conversation, at best. Indeed, as economists attempt to build ever more complex models these always take their point of departure in the representative agent. Especially, it is important to note that modern dynamic general equilibrium models are also fundamentally rooted in representative agent models and as such, these continue to represent the main work horse models in macroeconomics. Moreover, and I am speaking out of personal experience here; no respectable econ department today will accept a paper from their PhD or graduate students as "eligible" without proper neo-classical microfoundations. In this sense, the mathematical expression of representative agents remains the core tool in almost all macroeconomic analysis today (although this may about to change).
Take it to the Dumps?
Two obvious questions impose themselves at this point. One is whether the use of representative agents in macroeconomics has something, in general, to do with the recent soul searching among macroeconomists and the critique against the profession. And the second is whether the study of macroeconomics and demographics in particular calls for the non-use of representative agent modelling.
On the first I don’t necessarily think that it exists to the detriment of macroeconomics as a discipline, but I do think that a couple of points need mention. First of all I will echo the point made in Hartley (1997) that given the widespread use of representative agent modelling in almost all corners of macroeconomics and the almost religious devotion to it in graduate and PhD economics I think it is highly problematic that we have not had a more serious debate of its methodological merits. I would emphasize this in particular in the context of the fact that the use of representative agents leads to very inflexible (although rigorous) mathematical models and the blind faith in these models tend to steer macroeconomics onto a very narrow methodological path. During my research and initial ground work for the thesis I actually did write my own representative agent model to suit my specific agenda, but found in the end that I was paying more tribute to the laws of calculus than the connection between ageing and capital flows/open economy dynamics and as I set up the problem I ended up very close to the original benchmark problem.
On the second, I have not come to a decisive conclusion yet but I want to strongly emphasize that this is a very important question. The key transmission mechanism from demographics to the macroeconomy lies exactly in the aggregation of individual behaviour on the basis of life cycle and life course theory and at the moment, the only way that we are able to make such a link is through the representative agent. It is a fair question to ask here whether this is methodologically viable. For starters, we know that the representative agent in general suffers from aggregation bias and problems and as the aggregation of individual behaviour lies at the heart of taking life course and life cycle theory to the macroeconomy, it is an important question to ask. Another issue would be that at the current juncture life course and life cycle theory are built as bottom-up theories in the sense that they both invariably start on the micro level. But it does not need to be like this. The formulation of a pure macroeconomic theory on how demographics processes affect our economies is something worth thinking about and devoting resources to.
In the end I think that the use of representative agent modelling represent one of the core debates that macroeconomists must have in relation to the recent upheaval in the profession. It would be a mistake to consider me a one-sided opponent of representative agent modelling, but I am skeptical and more often than not I think that the representative agent represents more of a straitjacket than a rigorous economic tool. On the other hand, the rigorous treatment of economic problems that follows from the setup of representative agent models is also fundamentally appealing I think.
Ultimately, I am agnostic when it comes to the need for micro foundations. Clearly we need some form of micro oriented analysis when we study macro variables, but too much of a focus on the micro level may remove attention from complex processes whose main and only playing field is at the macro level. As such and while I would not advocate taking it to the dumps I think that the current macroeconomic debate should reflect a more nuanced view of the representative agent (and the use of Walrasian microfoundations) than is currently the case.
List of References
Colander, David (1996) – Beyond Microfoundations, Cambridge University Press; the book is a compilation of papers with David Colander as an editor of the entire volume.
Fisher, Irvin (1930) – The Theory of Interest
Friedman, Milton (1957) – A Theory of the Consumption Function, NBER
Harrod, Roy F (1939) – An Essay in Dynamic Theory, The Economic Journal, vol. 49, no. 193 (Mar,. 1939) pp. 14-33.
Harrod, Roy F (1960) – Second Essay in Dynamic Theory, The Economic Journal, vol. 70, no. 278 (Jun,. 1960) pp. 277-293.
Harrod, Roy F (1963) – Themes in Dynamic Theory, The Economic Journal, vol. 73, no. 291 (Sep,. 1963) pp. 401-421.
Hartley, James E (1996) – The Origins of the Representative Agent, The Journal of Economic Perspectives, Vol. 10, No. 2 Spring 1996 pp. 169-177
Hartley, James E (1997) – The Representative Agent in Macroeconomics, Routledge, Frontiers of Political Economy (1997)
Hugh, Edward (2006) – Rethinking the Demographic Transition, Working Paper
Kirman, Alan P (1992) – Whom or What Does the Representative Individual Represent? Journal of Economic Perspectives volume 6 no. 2 Spring 1992 pp. 117-136
Lucas, Robert E. Jr (1976) – Econometric Policy Evaluation: A Critique, Carnegie-Rochester Conference Series on Public Policy, issue 1 (Jan), pp. 19-46
Lucas, Robert E. & Rapping, Leonard (1970) – Real Wages, Employment and Inflation, In E. S. Phelps. ed. Microeconomic Foundations of Employment and Inflation Theory. New York: Norton, 1970.
Modigliani, Franco & Ando, Albert (1963) – The “Life Cycle” Hypothesis of Saving: Aggregate Implications and Tests, The American Economic Review, vol. 53, no. 1, part 1 (Mar., 1963) pp. 55-84
 – See links in this one for an overview of the initial flurry.
 – The main topic being international capital flows and ageing.
 – The point here is simply that for graduate economists, this problem is almost too simple but for many others it is unworldly. Here of course lies a great part of the problem!